Question

if the average weight of 4 students is 65 kg and the weight of 3 students is 60 kg, 65 kg, and 70kg respectively, then what would be the weight of the fourth student?​

Answer 1

Answer:

the fourth student is 65kg also

Step-by-step explanation:

how do we know this?

because

65+60+70+x/4 = 65

In order to find x

do 4 x 65 = 250

250 - (65+60+70) = weight of fourth student/x

x= 65kg

Answer 2

Given :

• We have been given that average weight of 4 students is 65 kg
• The weight of 3 students is given , 60 kg , 65 kg and 70 kg

To Find :

• We have to find the weight of the fourth student

Concept Used :

Average is the arithmetic mean of series of observations given.

Mathematically, it can be calculate by dividing the sum of observation to the total number of observations given

$\boxed{\sf{Average = \dfrac{Sum \: of \: Observations}{Number \: of \: Observations}}}$

Solution :

We have been given that average weight of 4 students is 65 kg

Using the above mentioned formula

$\longrightarrow \boxed{\sf{Average = \dfrac{Sum \: of \: weight }{Number \: of \: students}}}$

$\longrightarrow \sf{65 = \dfrac{Sum \: of \: weight}{4}}$

$\longrightarrow \sf{65 \times 4 = Sum \: of \: weight}$

$\longrightarrow \sf{260 = Sum \: of \: weight}$

$\longrightarrow \underline{\boxed{\sf{Sum \: of \: weight = 260}}}$

Hence, the sum of weight of all the 4 given students is 260

Let the weight of fourth student = x

• Weight of first student = 60
• Weight of second student = 65
• Weight of third student = 70

We have already found that

$\longrightarrow \sf{Sum \: of \: weight = 260}$

$\longrightarrow \sf{x + 60 + 65 + 70 = 260}$

$\longrightarrow \sf{x + 195 = 260}$

$\longrightarrow \sf{x = 260 - 195}$

$\longrightarrow \underline{\boxed{\sf{x = 65 \: kg}}}$

The weight of fourth student is 65 kg

$\underline{\boxed{\sf{\blue{Weight \: of \: 4th \: student = 65 \: kg}}}}$

$\large{\gray{\underline{\underline{\sf{Verification:}}}}}$

Average of the weight of students given as : 60 , 65 , 70 , 65

$\hookrightarrow \sf{Average = \dfrac{60+65+70+95}{4} }$

$\hookrightarrow \sf{Average = \dfrac{290}{4} }$

$\hookrightarrow \sf{Average = 65 \: kg }$

$\LARGE{\boxed{\mathfrak{\red{Hence \: Verified }}}} \: \: ✓$